Journal article Open Access

$\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov–Poisson–Fokker–Planck System

Addala, Lanoir; Dolbeault, Jean; Li, Xingyu; Tayeb, M. Lazhar


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{
  "DOI": "10.1007/s10955-021-02784-4", 
  "container_title": "Journal of Statistical Physics", 
  "title": "$\\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov\u2013Poisson\u2013Fokker\u2013Planck System", 
  "issued": {
    "date-parts": [
      [
        2021, 
        6, 
        21
      ]
    ]
  }, 
  "abstract": "This paper is devoted to the linearized Vlasov\u2013Poisson\u2013Fokker\u2013Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov\u2013Poisson\u2013Fokker\u2013Planck system without any small mass assumption.", 
  "author": [
    {
      "family": "Addala, Lanoir"
    }, 
    {
      "family": "Dolbeault, Jean"
    }, 
    {
      "family": "Li, Xingyu"
    }, 
    {
      "family": "Tayeb, M. Lazhar"
    }
  ], 
  "volume": "184", 
  "type": "article-journal", 
  "issue": "1", 
  "id": "5747811"
}
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